Eigenvalue Assignment by Static Output Feedback

Abstract

This paper investigates a new method for the search of a solution to the problem of eigenvalue assignment by means of static output feedback or, when there is no solution to this problem, for the synthesis of a minimal order controller that allows arbitrary pole placement. The aim of this work is an attempt to give an interpretation of the dynamical part of the control scheme in terms of unavailable information reconstruction such as minimal order observer design in single input system control problem. This study is based on a signal flow graph representation of the system. A first result concerns indications about redundant parameters in the output feedback gain matrix by inspecting independent subsystems. A second result gives a necessary condition for arbitrary eigenvalue assignment by static output feedback. More than a boolean verdict, this result provides with indications about the location of missing measured information in the system. Once the characteristic polynomial coefficients are expressed in terms of output feedback gains, it is possible to analyze the existence of a solution, at least locally, for the arbitrary eigenvalue assignment.